Math

Understanding Proficiency provides resources that guide educators in analyzing student work on performance tasks in order to develop a deeper understanding of the Common Core State Standards in mathematics.

What you’ll find:

Examples of student responses to Smarter Balanced mathematics performance tasks* — administered, scored and annotated by teachers — for all score levels and for all tested grades (grades 3–8 and high school)

Case studies that provide analysis of individual students’ work across all of the questions in the performance tasks, including samples from English learners (EL)

Select a grade level to explore grade-specific resources

About Smarter Balanced Math Performance Tasks

In order to gather evidence of college- and career-readiness, Smarter Balanced developed four “claims” that focus on students’ ability to understand and do math, as well as apply mathematical knowledge. Claims are broad statements of an assessment system’s learning outcomes. The Smarter Balanced Claims in mathematics cover both the content standards and the standards for mathematical practice within the Common Core State Standards. The performance task portion of the Smarter Balanced assessment is specifically designed to measure and gather evidence of students’ ability to apply mathematical knowledge to real-life situations in which they are required to problem solve, communicate their reasoning, analyze information and data, and model with mathematics. (The computer adaptive portion of the test focuses on grade-level mathematical content but it also includes the mathematical practices.)

Because the purpose of the performance task portion of the test is to assess evidence of claims 2, 3, and 4 (shown below), the tasks primarily rely on content skills studied in prior grade levels.

Smarter Balanced Mathematics Claims

1 Concepts & ProceduresStudents can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

2 Problem
SolvingStudents can frame and solve a range of complex problems in pure and applied mathematics.

3 Communicating
& ReasoningStudents can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

4 Data Analyisis
& ModelingStudents can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

Every performance task begins with a “Stimulus” that sets the context for the task and provides some of the data or parameters needed to complete the task. Every performance task includes four to six items, or questions, which are all connected to the Stimulus.

The first item (or first two items) of a task are intended as entry-level questions to prompt students to review and connect information provided within the Stimulus. Usually, student responses to these first items are machine-scored. Subsequent items are more complex, requiring synthesis of new information, analysis of results, modeling, explanation, and/or justification. Student responses to these more complex items are usually human-scored, using an item-specific rubric.

Some tasks have “dependent items,” meaning a response to one item depends on a response to a previous item. The scoring rules for dependent items instruct scorers to follow through with the student work from earlier items on which subsequent items depend: If the student incorrectly answers the earlier item, but then uses that response correctly in the dependent item that follows, the student would earn full credit for the dependent item. In this manner, the student is not penalized twice for the same mistake, and is rewarded for the mathematical thinking and problem-solving demonstrated in the dependent item.

Stimulus

Item 1

Item 2

Item 3

Item 4 (also connects to Item 5)

Item 5 (also connects to Item 4)

The diagram above represents a task in which Item 5 depends on Item 4. The performance tasks for Grades 5, 6, and 8 all provide examples of scoring dependencies.